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The integrated dual-function design is addressed in a Frequency Diverse Array-Phased Multiple-Input Multiple-Output (FDA-PMIMO) radar. Firstly, the transmit array is partitioned into multiple subarrays, where a tiny frequency shift is imported across different subarrays, while an identical carrier frequency is adopted within each subarray. At the design stage, the system parameters at the transmit side are optimized to accomplish joint range-angle estimation and mainlobe deceptive jammer suppression. Specifically, the subarray number and transmit weight matrix are devised to minimize the Cramér-Rao Lower Bounds (CRLBs) for estimation. In addition, the subarray number is optimized to maximize the Signal-to-Jammer-plus-Noise Ratio (SJNR) for jammer suppression. Subsequently, with the optimized architectures, the joint range-angle estimation is achieved based on the Maximum Likelihood (ML) criterion, and the jammers are suppressed via joint transmit-receive beamforming. At the analysis stage, the Root Mean Square Error (RMSE) as well as the output SJNR are analyzed to evaluate the performances of estimation and jammer suppression, respectively. Numerical results corroborate the effectiveness of the integrated dual-function design with the developed methods.

The problem of robust mainlobe deceptive jammer suppression in an element-pulse coding-multiple-input–multiple-output radar is explored utilizing data-dependent beamforming. In general, by introducing a tunable coding coefficient in both transmit elements and pulses, the response of mainlobe deceptive jammers can be identified as signals coming from different range ambiguity regions in the joint transmit–receive domain, and further mitigated through minimum variance distortionless response criterion. In specific, to address the problems of insufficient snapshots and polluted samples enrolled in data-dependent beamforming, a robust beamforming approach utilizing the two-dimensional atomic-norm minimization is proposed to estimate the steering vector corresponding to the signal of interest and to reconstruct the interference-plus-noise covariance matrix. In this regard, to reduce the computational burden, the alternating direction method of multipliers is utilized to obtain both the true target's angle error and the jammer-plus-noise subspace. In addition, a series of theoretical proofs including equivalent semidefinite program transformation, and the optimality conditions are provided. The validity of the proposed mainlobe deceptive jammer mitigation approach is confirmed through numerical results.

Space-time adaptive processing (STAP) is significant for detecting moving targets with phased array (PA) and frequency diverse array (FDA). However, the parameter estimation will be affected by the residual clutter. To mitigate this issue, this article puts forward an enhanced moving target parameter estimation method for STAP-based PA-FDA dual-mode radar, where dual-mode radar contains several advantages: it has simultaneously narrow-beam tracking and wide-beam searching capabilities and it can resolve range ambiguity problem with FDA mode and improve target detection performance with PA mode. With the dual-mode cooperative design, an accurate clutter covariance matrix is reconstructed to calculate weights for the maximum likelihood (ML) parameters estimator, where range-ambiguous clutter is considered. The Taylor series expansion of the ML estimator is developed to mitigate the problem of biased parameter estimation caused by residual clutter after suppression. Moreover, enhanced unambiguous range estimation is proposed with PA-FDA. Overall, the proposed method with PA-FDA enhances the parameters estimation performance of moving target. Simulation experiments are employed to demonstrate the validity of the proposed approach.

It is reported that the traditional frequency diverse array (FDA)-multiple-input–multiple-output (MIMO) radar has the capability of suppressing deceptive jamming delayed more than one pulse. However, mitigating the fast repeater deception jamming that distributed in the same range bin as the true target is intractable. To address this problem, the novel FDA-MIMO framework with a dual-frequency increment scheme is presented, where the whole transmit array is split into two subarrays with different frequency shifts. The subarray with smaller frequency increment is motivated to resolve range ambiguity. In contrast, the subarray with larger frequency increment is designed for combating fast-repeated jammer by increasing the range resolution. Moreover, maximum likelihood estimator is applied to obtain the joint range-angle estimation of target, where the adaptive beamforming weight vector is optimized under minimizing variance distortionless response criterion. The transmit spatial smooth method is incorporated to eliminate the component corresponding to the target, overcoming target cancellation issue. Extensive simulations are conducted to verify the superiority of the presented algorithm in mitigating fast repeater deception jamming.

By adopting the transmit minimum redundancy array in frequency diverse array multiple-input–multiple-output (FDA-MIMO), extra degrees-of-freedom in the transmit spatial domain can be obtained, owing to enlarged virtual elements. In this article, an interference suppression method is developed with the MR-FDA-MIMO radar using data-dependent beamforming based on virtual samples. In our designed method, both the transmit and receive beamforming are explored via a two-stage approach, including, at the receive beamforming stage, sidelobe interferences are first mitigated with minimum variance distortionless response-based beamforming after blocking the true target and mainlobe interferences. At the transmit beamforming stage, the samples from the physical array are divided into multiple subsets, while a difference coarray procedure is applied to each subset and multiple virtual samples are obtained to construct the interference-plus-noise covariance matrix. Furthermore, such a matrix is reconstructed based on the Capon spectrum. In addition, the errors for both the virtual samples and the virtual covariance matrix are analyzed. The proposed approach outperforms the traditional sparse smooth strategies in terms of suppressible interference number regardless of the number of physical array elements. The effectiveness of the proposed method for interference suppression is verified through numerical simulations.

With the rapid development of remote sensing (RS) technology, high-resolution RS image change detection (CD) has been widely used in many applications. Pixel-based CD techniques are maneuverable and widely used, but vulnerable to noise interference. Object-based CD techniques can effectively utilize the abundant spectrum, texture, shape, and spatial information but easy-to-ignore details of RS images. How to combine the advantages of pixel-based methods and object-based methods remains a challenging problem. Besides, although supervised methods have the capability to learn from data, the true labels representing changed information of RS images are often hard to obtain. To address these issues, this article proposes a novel semisupervised CD framework for high-resolution RS images, which employs small amounts of true labeled data and a lot of unlabeled data to train the CD network. A bihierarchical feature aggregation and extraction network (BFAEN) is designed to achieve the pixelwise together with objectwise feature concatenation feature representation for the comprehensive utilization of the two-level features. In order to alleviate the coarseness and insufficiency of labeled samples, a confident learning algorithm is used to eliminate noisy labels and a novel loss function is designed for training the model using true- and pseudo-labels in a semisupervised fashion. Experimental results on real datasets demonstrate the effectiveness and superiority of the proposed method.

This paper is focused on the problem of resolving the range ambiguity in a fixed phase coding-phased array (FPC-PA) radar. At the modeling stage, the FPC-PA radar is configured by a fixed phase coding in both transmit elements and pulses, where the transmit beam is modulated with a coding phase in each pulse. Then, after some appropriate signal processing procedures, the degrees-of-freedom (DoFs) in the transmit domain is obtained, and the range region numbers, namely the index of the range ambiguity region, are discriminated in the transmit spatial frequency domain. Particularly, echoes from different range ambiguity regions correspond to different pointing directions of the equivalent transmit beampattern. Moreover, in order to obtain the range ambiguity index and angle of the target, a three-stage algorithm is developed to enhance the performance against the effect of amplitude and phase errors. At the analysis stage, the parameter estimation performance is assessed in comparison with the Cramér-Rao lower bound (CRLB). Experimental and numerical results are provided to demonstrate the effectiveness of resolving range ambiguity and parameter estimation with the proposed method.

This article is focused on resolving the problem of suppressing mainbeam deceptive jammers in the element-pulse coding (EPC) radar. At the modeling stage, the element-pulse phase coding matrix (EPPCM) is employed at the transmit side, introducing extra coding degrees-of-freedom (DOFs) for the discrimination of the true target and mainbeam jammers. By utilizing the extra coding DOFs, nonadaptive and adaptive suppression method for mainbeam jammers are developed. Firstly, in order to suppress the jammers non-adaptively, the EPPCM is designed based on the coding steering vector orthogonalization (CSVO) method, which requires the identical angle of the true and false targets. Then, the adaptive suppression method is proposed for the general cases, where the angle deviation between the true and false targets occurs. To this end, the unitary EPPCM is designed to achieve the coding DOFs at the transmit side. Moreover, we take the towed radar active decoy (TRAD) jammer as an example and the sample selection scheme for the estimation of jammer-plus-noise covariance matrix is proposed. At the analysis stage, experimental and numerical results in terms of output signal-to-jammer-plus-noise ratio (SJNR) demonstrate the effectiveness of the devised methods for suppressing mainbeam deceptive jammers.

In this article, we investigate the problem of target localization with a multiple-input–multiple-output (MIMO) and frequency diverse array MIMO (FDA-MIMO) dual-mode radar system. The signal model for this newly introduced radar system is presented in detail. On this basis, a computationally efficient method for joint angle and range estimation is proposed by taking advantage of the subspace principle. First, the direction-of-arrival (DOA) of each target is determined by utilizing the fused signal data received via this dual-mode radar. In order to solve the coupling of target range and direction-of-departure (DOD) in FDA-MIMO radar mode, we use the monostatic-like characteristics of the dual-mode radar to develop an effective decoupling method. More specifically, by employing the same eigenmatrix corresponding to MIMO and FDA-MIMO radar data, the coupling of DOD and range in the FDA-MIMO mode can be easily overcome, and the parameters can be successively estimated with automatic paring. Further, to make full use of the transmit array for DOD estimation, we propose to compensate the range information in the transmit array steering vector to achieve an improved estimate of the target DOD. Extensive simulation results are performed to show that the proposed approach can provide superior DOD and range estimation accuracy while maintaining DOA estimation performance under the presented dual-mode radar system, and does not require the design of additional parameter pairing strategies with low computational cost, exhibiting excellent target localization behavior.

Ground moving target detection is one of the foremost tasks for multichannel synthetic aperture radar (SAR) system. The traditional robust principal component analysis (RPCA) method is capable of separating low-rank and sparse components from mixed echo signals, and it has been widely applied in SAR ground moving target indication (GMTI). However, it suffers from sensitivity to channel mismatch, high computational complexity, and excessively high false alarm rates. To address these issues, a novel method that combines adaptive multichannel data reconstruction (DR) with improved pseudo-skeleton decomposition (IPSD) is proposed. First, the iterative weighted approach is presented to precisely reconstruct the multichannel data vector with the joint-pixel model. After that, IPSD is presented to achieve the moving target detection, in which the row and column index sets are selected using the generalized inner product (GIP) and the amplitude histogram distribution criterion. Compared to the existing algorithms, the proposed algorithm effectively addresses the challenge of improving local region coherence in multichannel image sequences. In addition, compared to previous RPCA methods, the proposed algorithm significantly reduces false alarm rates in strong clutter backgrounds while achieving higher efficiency. Simulation results and real SAR data experiments validate the effectiveness of the proposed algorithm.

This article aims to investigate intelligent strategies of interference suppression for radar systems in the background of complex electromagnetic interferences. At the modeling stage, an interactive loop is established exploiting the interaction between the radar and the environment for interference suppression based on reinforcement learning. Specifically, the mappings from the interference suppression to the reinforcement learning, including the interference state set, the method set, evaluation criteria of interference suppression in different domains, and the principle of interference substate transformation, have been established. In this respect, two algorithms, including the Retroactive-Q (R-Q) learning and Retroactive-Deep Q Network (R-DQN), are developed by introducing a backtracking Q-value, which links the evaluations in each time step of a training round. At the analysis stage, the selection probabilities of the optimal implementation sequence for interference suppression are studied, and comparisons among the devised R-Q learning, R-DQN, conventional Q learning, and DQN are carried out in terms of output Q-values. Numerical results corroborate the effectiveness and robustness of the considered suppression strategies in diverse scenarios.

In this article, mainlobe deceptive jammer mitigation for multiple targets is investigated using a subaperture-frequency diverse array-multiple-input multiple-output (MIMO) radar. At the modeling stage, the transmit array is divided into multiple overlapped subapertures consisting of fully overlapped secondary subarrays, where a small frequency increment is introduced among different subapertures, while a phase coding modulation is adopted among different secondary subarrays. In this respect, all targets and jammers can be separated in a 3-D space-time cube, including the transmit spatial domain, the slow-time pulse domain, and the receive spatial domain. In this case, the problem of jammer mitigation is formulated, and a two-stage beamforming method is proposed, where the jammers with delayed pulses are first suppressed, and the jammers, which are located within the same transmit pulse, are further mitigated. Specifically, an alternating procedure is developed by transforming the suppression problem into several 1-D subproblems. In order to further improve the jammer mitigation performance, the subaperture transmit weights are also designed by maximizing the worst-case output signal-to-jammer-plus-noise ratio (SJNR) resorting to an iterative successive convex approximation (ISCA) algorithm. Numerical results corroborate the effectiveness of the developed methods in mitigating mainlobe deceptive jammers for the case of multiple true targets.

Separability is an important criterion for measuring the degree of overlap between different features in pattern recognition. Stronger separability indicates clearer feature margins, facilitating classification of samples into their respective classes. Therefore, if the separability of radar target echoes within the feature space increases, the likelihood of correct classification increases. A waveform with enhanced separability offers more reliable discrimination for specific targets and highlights their unique aspects. Accordingly, this paper proposes radar waveform design methods driven by target echo pattern separability, i.e., the convolution of the target high-resolution range profiles (HRRP)/target impulse response (TIR) and transmit waveform. First, from the views of local HRRP/TIR manifold structure preservation and inter-class distance enlargement, we construct a minmax based fractional optimization model with non-convex and non-linear orthonormality and constant modulus (CM) constraints. Then, the derived waveform design solution is computed iteratively via subproblem division, fraction simplification, and high-order polynomial optimization. Furthermore, we extend our study to a linear discriminant analysis-based waveform design model, which incorporates minmax intra-class distance and inter-class distance metrics to maximize separability of all classes from a worst-case perspective. We utilize simulated datasets based on the scattering point model as well as electromagnetic simulation and MSTAR CSV datasets to evaluate the performance of our waveform design approaches.

In this article, the problem of detecting the true target in the background of mainlobe deceptive jammers is addressed in a frequency diverse array multiple-input multiple-output (FDA-MIMO) radar. At the modeling stage, a simultaneous detection and discrimination method is formulated by utilizing the specific range degrees of freedom DOFs of the FDA-MIMO radar. In this respect, the detection problem for the window under test (WUT) is formulated as a multihypothesis test, where the alternative hypothesis is composed of possible true and false targets. In particular, the true target is discriminated from the mainlobe jammers as a byproduct. At the design stage, detectors are designed resorting to a suboptimal way, i.e., penalized log-likelihood ratio test. To obtain the maximum likelihood (ML) estimate of unknown parameters, the data in the transmit and transceive domain are jointly utilized. At the analysis stage, the detection performance as well as the discrimination performance are analyzed with comparisons among the proposed detectors and the competitors. Simulation results demonstrate the effectiveness of the proposed detectors.

Although the problem of range ambiguity is solved with the frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radar by utilizing the degree-of-freedom in the range domain, the phenomenon of Doppler ambiguity occurs for the fast-moving target. In this article, an offset frequency alignment method is proposed to solve the problem of Doppler ambiguity in FDA-MIMO radar. At the design stage, the Doppler frequency offsets, corresponding to different transmit pulses, are aligned by eliminating the residual phases. In this regard, the point targets can be focused in the transmit spatial frequency domain. Furthermore, the Doppler ambiguity index is estimated after principal velocity compensation resorting to a maximum likelihood criterion, where both the cases of known and unknown range ambiguity indexes are investigated, respectively. Moreover, in order to ensure the estimation performance, the frequency offset across the transmit array elements is designed by enlarging the term related to the Doppler frequency offset. At the analysis stage, the performance of Doppler ambiguity index estimation in terms of the root-mean-square error is assessed in comparison with the Cramer–Rao bound. Numerical results are provided to verify the effectiveness of the proposed method to resolve the Doppler ambiguity.

In the conventional array radar, the suppressible interference is generally limited by the array element number, referred to as the degree of freedom (DOF) of the array. Similarly, the suppressible number of deceptive interference is limited by the transmit element number of frequency diverse array (FDA) multiple-input multiple-output (MIMO) radar. In this article, an interference suppression method based on data-independent beamforming is proposed with FDA-MIMO radar by using a minimum redundancy array (MRA) design in its transmit port, referred to as MR-FDA-MIMO radar. This break through the limitation on the number of suppressible deceptive interferences. The MRA is employed to obtain extended DOF by using difference coarray, resulting in the suppressible number of order O(2M) with M transmit element number. The beamforming method consists of two manifolds: 1) in the receive beamforming stage, the possible target is preserved by using orthogonal subspace projection and the sidelobe barrage interference is suppressed; and 2) in the equivalent transmit beamforming stage, possible nonideal factors are taken into consideration for constructing the covariance matrix to widen the notches corresponding to the predicted deceptive interference. The proposed method outperforms in terms of number of the suppressible deceptive interferences and the signal-to-interference-plus-noise ratio, which is demonstrated with simulation examples.

This article proposes a cognitive frequency diversity array (FDA) multiple-input multiple-output (MIMO) (FDA-MIMO) radar network (CFDA-MIMON) target discrimination and tracking algorithm under main-lobe deceptive trajectory interference. This algorithm can be divided into two stages: search-discrimination-initialization and cognitive target tracking. The first stage mainly uses the distribution characteristics of target and main-lobe deceptive trajectory interference on different radars to discriminate the target and interference in the radar network. A target state initialization strategy driven by G-pair measurements with large time interval is proposed for target tracking. In the second stage, a cognitive target tracking algorithm of single FDA-MIMO radar system is designed based on the criteria of maximum Capon power spectrum. In addition, in order to avoid the divergence problem of the extended Kalman filter, a target state correction method based on auxiliary particles is proposed. Finally, the fusion strategy of multiple radar trajectories is used to alleviate the estimation error of the single radar. Numerical experiments verify that the proposed CFDA-MIMON target discrimination and tracking algorithm can distinguish the target from main-lobe deceptive trajectory interference without prior information of the target, and output the target's trajectory.

High-aspect-ratio square optical fiber arrays enable massive applications from nanoscale to mesoscale, while fabrication is becoming a challenge. Here, a simple and inexpensive method is proposed based on capillary-induced self-assembly and tailored external constraints. The steady-state solution of the liquid morphology equation indicates that the interaction between optical fibers and liquid drives the array into shapes with lower free energy. Therefore, a well-designed external constraint, which affects the balance between capillarity and elastic restoration, can regulate the final arrangement of the optical fibers. Based on the dynamic analyses of the droplet-to-column transitions, liquid flow along optical fibers, and approach of optical fiber driven by liquid bridge and viscous damping, the factors influencing the capillary-induced self-assembly process are investigated, and the fabrication conditions are thus optimized. Experimental results verified the proposed method. The fabricated vector tactile sensing probe achieves a square array with aspect ratios of ~135. Its displacement resolutions in three dimensions are proven better than 60 nm.

This letter focuses on discriminating true target from mainlobe jammers using a frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar. To this end, a three-stage detection and discrimination architecture is proposed. Specifically, mainlobe jammers caused by large time delays can be discriminated from the true target based on the range degrees-of-freedom (DOFs) of FDA-MIMO radar, while the true target and jammers generated with small time delays are distinguishable in the fast time domain. In particular, a binary hypothesis test is formulated for discrimination, where the $H_{1}$ hypothesis contains the true target, while the $H_{0}$ hypothesis contains the unknown mainlobe jammer. The mainlobe jammer can be formulated as either a known subspace model or an unknown rank-one model. The former leads to a subspace-based selective detector (SSD) and the latter generates a rank-one-based SD (ROSD). Then, the formulated tests are handled using the generalized likelihood ratio test (GLRT) criterion. At the analysis stage, the selectivity and detection performance are compared with the conventional GLRT and selective receivers. Simulation results validate that the proposed detectors achieve satisfactory detection performance while providing the selectivity to mainlobe jammers.

In this letter, the problem of adaptive target detection for a frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar in the presence of unknown mutual coupling (MC) is investigated. Unlike the conventional phased array (PA) radar, the signal model of FDA-MIMO radar in unknown MC is constructed using two symmetric Toeplitz matrices accounting for the effects of unknown MC at the transmitter and receiver. At the formulation stage, the detection problem is formulated as either a binary hypothesis test or a multi-hypothesis test. The former is tackled based on the generalized likelihood ratio test (GLRT) leading to a robust detector (RD). The latter resorts to the penalized test and multifamily LRT (MFLRT), resulting to Modified-Multiple Hypothesis Penalized Likelihood Ratio Test (M-MHPLRT) and MFLRT detectors, respectively. At the analysis stage, the effectiveness of the developed detectors is verified with comparisons among the benchmarks and existing detectors via Monte Carlo simulation results.

Forward-looking mode for moving target detection is important for airborne radar systems, however, it is difficult to suppress the range-dependent clutter in the presence of range ambiguity using the traditional space-time adaptive processing (STAP) techniques. In this article, a vertical coherent frequency diverse array (FDA) radar using quadratic phase coding (QPC) is proposed to alleviate the range-ambiguous clutter problem. The proposed vertical coherent FDA radar has two major advantages: 1) it uses an identical baseband waveform for each transmit element, which prevents the unreal orthogonal waveform assumption in the multiple-input multiple-output (MIMO) framework and 2) it achieves wide spatial coverage in elevation within a single-pulse duration, which is desirable for the airborne reconnaissance radar. The space-frequency-coupled characteristic of vertical coherent FDA is revealed and a series of two-dimensional (2-D) matched filters are designed, which is helpful for range-ambiguous clutter separation. Based on the QPC technique, the residual clutter is suppressed by orthogonal projection (OP) filtering, which further improves the target detection performance. With the proposed vertical coherent FDA using QPC, the range-ambiguous clutter can be separated successfully, and the clutter suppression performance is improved. Simulation results are presented to verify the effectiveness of the proposed method in serious range-ambiguous clutter scenarios.

For the high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) system, the increasing imaging width results in a serious range ambiguity problem, which affects the performance of ground moving target indication (GMTI). In this article, a novel nonuniform subpulse coding (NSPC) scheme is proposed. It is characterized by resorting to range-frequency band resources and detailed coding design for each subpulse, enabling the beam auto-scanning in elevation. Also, the bandpass filtering and digital beamforming (DBF) technology with improved data reconstruction are utilized to realize the separation of subpulses and suppress range ambiguity. The NSPC technique exchanges the signal bandwidth for increasing swath without range ambiguity, and the coded subpulses can be directed to the prescribed regions, while skipping the invalid areas where the echoes are blocked. After that, through the robust principal component analysis (RPCA) method, the moving target detection is performed for each separated region without residual range-ambiguous interference. The proposed approach has been theoretically deduced in detail and the simulation experiments demonstrate its effectiveness.

In this article, two novel methods for synthetic aperture radar (SAR) image super-resolution (SR) are proposed. The main challenge for SAR image SR reconstruction is speckle noise. For this reason, a novel algorithm termed the importance sampling cubature Kalman filter (ISCKF) is proposed to reconstruct a high-resolution (HR) image from a series of low-resolution (LR) images. However, as the reconstructed image usually embraces residual noise visually, we establish a nonlinear low-rank optimization model in order to further reduce the speckle noise drastically. Correspondingly, an alternating direction method of multipliers based on the low-rank model (ADMM-LR) algorithm is proposed to solve it, which yields the other novel method termed ISCKF + ADMM-LR for SAR image SR. In addition, we establish the computational complexity of the proposed algorithms. The experimental results of both the simulated images and real SAR images demonstrate that the performance of the proposed methods is superior to some state-of-the-art methods in both SR and despeckle.

In this article, we exploit a granular-based modeling scheme to realize the number of sources detection under nonideal conditions (in low signal-to-noise ratio levels and small snapshots scenarios), in which the idea of information granules and granular computing is integrated with the fuzzy set theory. In the developed scheme, a collection of eigenvalues, which is calculated by the array output correlation matrix, is constructed as a time series. Then, the principle of justifiable granularity criterion is introduced to split the time series into two regions so as to establish a set of upper and lower bounds of prototypes for the signal and noise subspaces. Subsequently, the fuzzy C-means-based encoding and decoding mechanism is employed to optimize the prototypes. During this process, the encoding mechanism is used to produce a pair of information granules, and the decoding mechanism is used to evaluate the quality of information granules. After several rounds of iteration, an optimized prototype vector and a partition matrix are generated. Finally, the structure of the time series is exposed (encoded into) by an optimized prototype vector and a partition matrix, and the number of sources can be determined conveniently through the partition matrix. Simulation results show that the proposed method outperforms the commonly used methods under nonideal conditions.

The transmit antenna beampattern of the phased array radar is only a function of angle, limiting its ability to discriminate the targets from the same direction. Recently, the waveform diverse array radars expand the angle-dependent beampattern to an angle-time-range-dependent three-dimensional function by modulating the frequencies/time delays/phases across different transmit antenna elements. In this respect, extra Degrees-of-Freedom (DOFs) in the range domain are achieved, which opens up an innovative way to fulfil the tasks with enhanced system performance by jointly using the angle and range information. This paper summaries the developments of waveform diverse radars, including the Frequency Diverse Array (FDA), the Space-Time-Circulating-Array (STCA), and the Element-Pulse-Coding (EPC) frameworks, with emphasis on the analysis of the range-dependent beampattern from the basic properties upon how it is controlled. Moreover, the most recent advances of utilizing such a range-dependent beampattern in target detection, parameter estimation and identifiability, clutter suppression, jammer suppression and Synthetic Aperture Radar (SAR) imaging are discussed.

The problem of mainlobe deceptive jammer suppression with a novel stepped frequency (SF)-receive delay array (RDA) radar is addressed in this paper. In our system design, the linear frequency modulation (LFM) waveform with a SF across the antenna elements is transmitted in a uniform linear array, and the received echo is delayed with a time shift between adjacent antenna elements, introducing extra range-dependent degrees-of-freedom (DOFs) in both transmit and receive domains. Consider a typical form of mainlobe jammers, where multiple false targets are generated in the same transmit pulse or same range bin behind the true target after short time modulation. In this respect, the jammers are discriminated from the true target in the joint transmit-receive spatial frequency domain, and suppressed via a data-dependent beamformer based on the minimum variance distortionless response (MVDR) criterion. To further solve the problem of sample selection due to the pseudo-random distribution of the false targets, two kinds of robust beamformers based on the enhanced Capon power spectrum (ECPS) and the eigen-projection elimination (EPE), are developed to reconstruct the jammer-plus-noise covariance matrix and estimate the steering vector of the true target. The performance of the proposed methods in suppression of mainlobe deceptive jammers is evaluated via numerical simulations and compared with the existing systems and robust beamforming methods.

The perfectly partly calibrated antenna array is a frequently assumption in most of the existing array gain/phase calibration methods. In practice, however, the partly calibrated array is usually not available. In this letter, a tail optimization method for direction finding with unknown gains and phases in the presence of spatially non-uniform noise is proposed. Specifically, the unknown gain/phase entry is firstly merged into the signal power by using the sparse representation. Subsequently, a tail optimization method that can significantly suppress the occurrence of pseudo-peaks is designed to determine the signal DOAs without a priori information of unknown sensor gain and phase errors. In addition, the spatially non-uniform noise can be removed by a linear transformation to improve the robustness against the noise. Numerical simulations examples are presented to demonstrate the effectiveness and superior performance of the proposed approach over the other existing counterparts.

Range-ambiguous clutter suppression is challenging for airborne radar in non-sidelooking geometry. The target detection performance might degrade severely due to range ambiguity and range dependence problems. It is proved that the frequency diverse array (FDA) is capable of resolving the range ambiguity and is beneficial for range ambiguous clutter suppression. However, FDA uses wide coverage transmit beampattern, which causes somewhat gain loss compared to the phased array (PA). In this paper, we establish a PA-FDA dual-mode radar to maximize the advantages of PA and FDA radars to improve target detection performance in range-ambiguous clutter scenario. Firstly, the range ambiguous resolvability of FDA is utilized, where range ambiguous clutters are separated by using pre-filtering before space-time adaptive processing. Therefore, the range dependence compensation algorithms can be performed independently to further address the range dependence problem of non-sidelooking array radar. In this case, the clutter covariance matrix (CCM) is reconstructed by using linear combination of distinguishable CCMs corresponding to different range regions, resulting in improved accuracy of CCM estimation. Secondly, the enhanced CCM is applied in PA counterpart, which maximizes the high beampattern gain of PA and range ambiguity resolvability of FDA. It is verified that the PA-FDA dual-mode radar outperforms the PA or FDA single-mode in simultaneously narrow-beam detection and wide-angle coverage. Thus, the proposed PA-FDA dual-mode radar can greatly contribute to searching and tracking tasks. Simulation examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the traditional multi-target multi-Bernoulli (MeMBer) filter, only the radar signal after constant false alarm rate (CFAR) is considered. In addition, it is also necessary to assume that the detection probability of the target and the covariance matrix of the measurement noise are known. In fact, the detection probability of the target and the covariance matrix of the noise are difficult to determine. Therefore, this paper proposes an improved labeled multi-target multi-Bernoulli (IL-MeMBer) filter that can avoid considering the detection probability of the target and the covariance matrix of the measurement noise. Firstly, the multi-target superposition measurement model of FDA-MIMO is given in the presence of false targets. Secondly, the target likelihood function under the superposition measurement model is derived by analyzing the characteristics of the traditional point measurement likelihood function and the Music spatial spectrum. Thirdly, considering the unknown and time-varying number of targets, the original echo signals without detection probability before (CFAR) processing, and no target tracks output by the traditional MeMBer filter, we put forward an analytical solution of the IL-MeMBer filter. Finally, a fusion strategy based on Euclidean distance is proposed to solve the problem that the same target can be estimated to have multiple tracks in the IL-MeMBer filter. In addition, the sequential Monte Carlo (SMC) implementation of the IL-MeMBer filter is provided. Numerical experiences verify the effectiveness and superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

The performance of space–time adaptive processing (STAP) radar degrades dramatically when the target occurs in the training data. Traditional robust linearly constrained minimum variance (LCMV) STAP method uses magnitude constraint to maintain the mainlobe of the STAP beamformer. In this paper, a joint magnitude and phase constrained (MPC) STAP method is proposed with the phase constraint incorporated in the response vector of the beamformer. The explicit expression of the phase constraint is derived by exploring the conjugate symmetric characteristic of the adaptive weights. With joint magnitude and phase constraints imposed on several discrete points in the mainlobe region, the MPC-STAP approach has good robustness against target contamination. In addition, the linear-phase response can be guaranteed by the proposed method, which provides distortionless response in both spatial and temporal domains. Simulation results are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The performance of space–time adaptive processing (STAP) may degrade dramatically if some undesired mismatches exist in real scenarios, such as array calibration error, distorted antenna shape, direction of arrival (DOA) and Doppler frequency mismatches between the actual and presumed responses to the desired target signal, insufficient training data samples and so on. In this paper, we develop a new approach to STAP that is robust to different variations in real scenarios. This method is based on the iterative optimization for the spatial–temporal separate filter. It is confirmed that this method belongs to the class of colored loading algorithms. The loading factor can be efficiently calculated based on the known level of the uncertainty mismatch sets of spatial temporal steering vectors. Computer simulations demonstrate that the proposed robust two-dimensional (2-D) beamformer with colored loading has attained better performance as compared to the conventional STAP algorithm. [ABSTRACT FROM AUTHOR]

Frequency diverse array (FDA)-multiple-input and multiple-output (MIMO) radar is characterized with a range-angle-dependent transceive beampattern by introducing incremental frequencies among the transmit array elements and separating the transmitted waveforms with matched filtering in the receiver. In this respect, the paper aims to control the range-angle-dependent transceive beampattern for FDA-MIMO radar by designing the weight vector according to the desired response. At the design stage, the weight vectors to control the beampattern responses of different regions are devised by performing the orthogonal decomposition technique. Then, a filtering matrix using the oblique projection operator is constructed to filter the weight vectors for different regions, where two iterative algorithms are developed either considering concurrent or successive control of multiple regions. In such a way, a desired range-angle-dependent transceive beampattern is formed with simultaneously broadened nulls and a flat-top mainlobe. At the analysis stage, the method has been applied to interference mitigation in FDA-MIMO radar, where the mismatch exists both in the sidelobes and mainlobe. Simulated and measured results are provided to corroborate the effectiveness of the proposed methods.

Abstract: To counter the problem of acquiring and processing huge amounts of data for synthetic aperture radar (SAR) using traditional sampling techniques, a method for sparse SAR imaging with an optimized azimuthal aperture is presented. The equivalence of an azimuthal match filter and synthetic array beamforming is shown so that optimization of the azimuthal sparse aperture can be converted to optimization of synthetic array beamforming. The azimuthal sparse aperture, which is composed of a middle aperture and symmetrical bilateral apertures, can be obtained by optimization algorithms (density weighting and simulated annealing algorithms, respectively). Furthermore, sparse imaging of spectrum analysis SAR based on the optimized sparse aperture is achieved by padding zeros at null samplings and using a non-uniform Taylor window. Compared with traditional sampling, this method has the advantages of reducing the amount of sampling and alleviating the computational burden with acceptable image quality. Unlike periodic sparse sampling, the proposed method exhibits no image ghosts. The results obtained from airborne measurements demonstrate the effectiveness and superiority of the proposed method.

Abstract: Fast time (range delay time) information has been well exploited for the terrain scattered interference or hot clutter mitigation. In this paper, an approach incorporating fast time in space–time adaptive processing (STAP) is introduced for monostatic (cold) clutter rejection. This method takes advantage of the coherence information of adjacent range bins. Compared to traditional STAP algorithms, the performance of monostatic clutter mitigation can be improved due to the fact that the additional range degree of freedom (DoF) can mitigate various deleterious factors in realistic scenarios which may increase the DoFs of clutter patches. Results of real measured data processing using airborne X-band and MCARM radar systems demonstrate the effectiveness of the proposed processor. [Copyright &y& Elsevier]

Multiple clusters of particles characterized in terms of fixed-position and fixed-distribution are utilized for target capture, target state estimation, and track maintenance in traditional particle filters. It is often unsustainable in target acquisition and track maintenance since the prior information of target is hard to acquire. In addition, the obtained measurement information may be fuzzy (interval measurement) in practical engineering applications. This is also a challenge in traditional particle filters. In view of these two problems, a novel measurement-driven AParticle- δ -GLMB-IM filter is proposed. The AParticle- δ -GLMB-IM filter uses RLF to determine the affiliation between the survival targets and the interval measurements. A newborn label or a survival label will be given to the newborn particles driven by the same single interval measurement. Furthermore, this paper presents a new box particle application named ABox- δ -GLMB filter. Numerical experiments verify the effectiveness and superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

• Jointly optimizing covariance matrix and mutual coupling. • Utilizing least square criterion to eliminate non-uniform noise. • Using subspace decomposition theory to obtain the mutual coupling matrix. • Determining DOAs of coherent signals in mutual coupling and non-uniform noise. It is well known that classic direction-of-arrival (DOA) estimation methods yield poor accuracy and low resolution in the presence of mutual coupling and non-uniform noise. To tackle this problem, a DOA estimation method for jointly optimizing noise-free covariance matrix and mutual coupling coefficient is proposed in this paper. Based on the least squares (LS) criterion, the signal subspace and noise-free covariance matrix under mutual coupling can be obtained in an iterative manner. With the determined signal/noise subspace, the mutual coupling matrix can be reconstructed and the covariance one is estimated after mutual coupling compensation. Finally, the noise-free covariance matrix is preprocessed by spatial smoothing strategy and then used to determine the DOAs with the help of traditional DOA estimators. Compared to the conventional DOA estimation methods, simulation results demonstrate that, the proposed method can suppress the non-uniform noise significantly, alleviate the effect of mutual coupling on spatial smoothing technique obviously, as well as improve the DOA estimation performance in the case of coherent signals considerably. [ABSTRACT FROM AUTHOR]

Ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler ambiguity and azimuth spectrum split caused by target unknown motion parameters. To handle these problems, we propose a fast non-searching method for maneuvering target refocusing and motion parameters estimation in this paper. First, the azimuth-deramp is conducted, which is capable of eliminating the azimuth spectrum splitting. In the sequel, the second-order keystone transform (SOKT) based on the scaling principle is applied to further correct the residual range curvature. Then, the phase difference (PD) is performed to eliminate the range walk and estimate the motion parameters, which does not require the prior knowledge of Doppler ambiguity number. Finally, the moving target can be well focused with the estimated parameters. This method has high computational efficiency and improved parameter estimation accuracy. Both simulated and real data are processed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In practical application, the time when the maneuvering targets enter and leave the radar coverage observation is usually unknown, which will seriously deteriorate the performance of coherent integration and target detection. To solve this problem, we propose a method based on the symmetric autocorrelation function and the proposed window Lv's transform (SAF-WLVT) for coherent integration and motion parameters estimation of maneuvering target, involving the range migration (RM) and Doppler frequency migration (DFM). Firstly, the SAF is utilized to correct the linear RM induced by target's radial velocity and range curvature caused by target's radial acceleration simultaneously. Then, the proposed WLVT is applied to eliminate the residual DFM caused by the target's radial acceleration, accumulate the target energy without introducing excess noise energy, and obtain the baseband velocity and acceleration estimations. Finally, the Doppler ambiguity number is estimated by matched filtering and 1-D parameter searching, and then the target's radial velocity is obtained. The proposed method has low computational complexity, and possesses favorable performance of target detection and parameter estimation in the high signal to noise (SNR) environment. The mathematical analysis and simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithm based on the inverse model (IM-MOEA) is a popular method to solve multi-objective optimization problems (MOPs). However, IM-MOEA has some drawbacks such as low accuracy and difficulty in dealing with MOPs with irregular PFs. To address these issues, adaptive reference vector mechanism and nonrandom grouping strategy are employed in IM-MOEA, which enhances the reliability of the inverse model. In addition, a modified selection mechanism is used to choose candidate solutions. Further, an enhanced IM-MOEA with adaptive reference vectors and nonrandom grouping (AN-IMMOEA) is proposed in this paper. The experimental results on 27 MOPs indicate that the proposed method has a better performance than other MOEAs. [ABSTRACT FROM AUTHOR]

In a multiple-input multiple-output (MIMO) radar, it is desired to maximize the power radiation in an angular region of interest, which, however, is hardly achievable because a set of orthogonal waveforms is employed at the engineering. Different from traditional colocated MIMO radar, space-time coding array (STCA) transmits an identical waveform with a tiny time delay circulating across array elements. It can provide a simple way to achieve the full angular coverage with a stable gain. In this paper, a new scheme referred to as chirp-STCA is proposed to synthesize the desired beampattern flexibly. With the quantitative relationship between the time delay and the span of beam spreading, the transmit beampattern synthesis issue is converted to the design of time delay value which can be readily realized based on the framework of chirp-STCA. As a result, the desired angular sector coverage of the radiation power can be realized by setting a proper time delay. The proposed chirp-STCA can provide many desired features including low range sidelobe level, low computational complexity, and constant modulus. In addition, the range-angle properties are examined by analyzing the transmit beampattern response and the ambiguity function. Numerical results are presented to demonstrate the effectiveness and simplicity of the chirp-STCA scheme for the transmit beampattern synthesis. [ABSTRACT FROM AUTHOR]